This is an abstract of a presentation at The 8th International Congress on Math Education (ICME 8), July 14-21, 1996 in Seville, Spain..
I investigate how children understand concepts and the meaning of symbolic representations when working with conceptual models (with the OPERA system) vs. with formal models (with the spreadsheet). The particular focus of this study is the nature of student conversation when collaborating to solve tasks embodied in such systems. My approach focuses theoretical attention on the nature of conversational turn taking between children working one of the two computer tools.
This study shows that conversational processes of acceptance stemmed from collaborative learning, and that those processes enabled the construction of shared meaning resulting in the development of the concept of operator (with the OPERA system), and the concept of algebraic formula (with the spreadsheet). For both systems, one participant described a property of the model created a shared meaning. The other participants then accept the meaning uttered by the first participant and refine it. A second process is a process of convergence that is initiated by an impasse within one representation and is characterized by a change of representation. The third turn-taking occurrence is a process of confirmation through a different representation. The talk will concentrate on these three processes and on the differences between the conceptual and the formal model.
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